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Mathematics : Application of Derivatives

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

Long Answer Type

261.

Find the maximum and minimum value of x + sin 2 x on $left square bracket 0 comma space 2 straight pi right square bracket$ .

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Short Answer Type

262.

Find both the maximum value and the minimum value of
3x⁴ – 8x³ + 12x² – 48x + 25

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263. It is given that at x = 1, function x⁴ – 62x² + ax + 9 attains its maximum value, on the interval [0, 2], Find the value of a.

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Long Answer Type

264.

straight y space equals space fraction numerator ax minus straight b over denominator left parenthesis straight x minus 1 right parenthesis thin space left parenthesis straight x minus 4 right parenthesis end fraction

has a turning point at P(2, -1). Find the values of a and b and show that y is maximum at P.

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265. If y = a log | x | + bx² + x has its extremum values at x = – 1 and x = 2, find the values of a and b. Prove that these extrema are maximum.

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Short Answer Type

266.

Find the maximum and minimum values of $fraction numerator log space straight x over denominator straight x end fraction space in space 0 less than straight x less than infinity$ .

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Long Answer Type

267.

Find the shortest distance of the point (0, c) from the parabola y = x² , where 0 ≤ c ≤ 5.

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Short Answer Type

268. An Apache helicopter of enemy is flying along the curve given by y = x² + 7. A soldier, placed at (3. 7), wants to shoot down the helicopter when it is nearest to him. Find the nearest distance.

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Multiple Choice Questions

269.

For all real values of x, the minimum value of $fraction numerator 1 minus straight x plus straight x squared over denominator 1 plus straight x plus straight x squared end fraction$ is

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270.

The maximum value of $open square brackets straight x left parenthesis straight x minus 1 right parenthesis space plus space 1 close square brackets to the power of 1 third end exponent comma space space space 0 space less or equal than space straight x space less or equal than space 1$ is

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