Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Application of Derivatives

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Short Answer Type

221.

Find the maximum or minimum values, if any, of the following functions without using the derivatives:
16x²– 16x + 28

91 Views

222.

Prove that the following functions do not have maxima or minima:
f(x) = e^x

101 Views

223.

Prove that the following functions do not have maxima or minima:
g(x) = log x

86 Views

224.

Prove that the following functions do not have maxima or minima:
h(x) = x³ + x² + x + 1

81 Views

225.

Find the absolute maximum value and the absolute minimum value of
$straight f left parenthesis straight x right parenthesis space equals space 1 third straight x cubed minus 3 straight x squared plus 5 straight x plus 8 space in space left square bracket 0 comma space 4 right square bracket.$

77 Views

226.

Find the absolute maximum and minimum values of a function f is given by
f (x) = 2x³ – 15x² + 36x + 1 on the interval of [1, 5].

91 Views

Long Answer Type

227. Find absolute maximum and minimum values of a function f given by

straight f left parenthesis straight x right parenthesis space equals space 12 straight x to the power of 4 over 3 end exponent space minus space 6 straight x to the power of 1 third end exponent comma space space space straight x space element of space space space open square brackets negative 1 comma space 1 close square brackets

73 Views

Short Answer Type

228.

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:
$straight f left parenthesis straight x right parenthesis space equals space straight x cubed comma space space space straight x space element of space left square bracket negative 2 comma space space 2 right square bracket$

87 Views

229.
Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:
$straight f left parenthesis straight x right parenthesis space equals space sin space straight x plus space cosx comma space space straight x space space element of space space left square bracket 0 comma space straight pi right square bracket$

Here $straight f left parenthesis straight x right parenthesis space equals space sin space straight x plus space cos space straight x$
It is differentiable for all x in $open square brackets 0 comma space space straight pi close square brackets$
$therefore space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space cosx minus space sinx space space space space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 0 space gives space cosx minus space sinx space equals space 0 therefore space space space sin space straight x space equals space cosx space space space space or space space space space space tan space straight x space equals space 1 space space space space space space space rightwards double arrow space space space space straight x space equals space straight pi over 4 space element of space space space open square brackets 0 comma space straight pi close square brackets space space space space space space straight f open parentheses straight pi over 4 close parentheses space equals space sin space straight pi over 4 plus space cos space straight pi over 4 space equals space fraction numerator 1 over denominator square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 end fraction space equals space fraction numerator 2 over denominator square root of 2 end fraction space equals space square root of 2 straight f left parenthesis 0 right parenthesis space equals space sin space 0 plus space cos space 0 space equals space 0 plus 1 space equals space 1 straight f left parenthesis straight pi right parenthesis space equals space space sin space straight pi space plus space cos space straight pi space equals space 0 minus 1 space equals space minus therefore space space space absolute space max. space value space space equals space square root of 2 space and space absolute space min. space value space space equals space minus 1.$

77 Views

230.

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:
$straight f left parenthesis straight x right parenthesis space equals space 4 straight x minus 1 half straight x squared comma space space space straight x space element of space open square brackets negative 2 comma space space 9 over 2 close square brackets$