Find the slope of the tangent to the curve . from Mathematics

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 Multiple Choice QuestionsShort Answer Type

51.

Find the points on the curve y = x3 at which the slope of the tangent is equal to the y-coordinate of the point.

 
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52. Find the slope of the tangent to the curve x = at2, y = 2at at  t = 1.
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53.

Find the slope of the tangent to the curve y = x3 – x at x = 2.

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54.

Find the slope of the tangent to the curve y = 3x4 – 4x  at (i) x = 1 (ii) x = 4.

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55.

Find the slope of the tangent to the curve straight y space equals fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction comma space space space straight x not equal to space 2 space space at space straight x space equals space 10.


The equation of curve is
                     straight y space equals space fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction comma space space space space space space straight x space not equal to space 2
therefore space space space space space space dy over dx space equals space fraction numerator left parenthesis straight x minus 2 right parenthesis. space begin display style straight d over dx end style left parenthesis straight x minus 1 right parenthesis minus left parenthesis straight x minus 1 right parenthesis begin display style straight d over dx end style left parenthesis straight x minus 2 right parenthesis over denominator left parenthesis straight x minus 2 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space space space space space equals space fraction numerator left parenthesis straight x minus 2 right parenthesis. space 1 minus space left parenthesis straight x minus 1 right parenthesis. space 1 over denominator left parenthesis straight x minus 2 right parenthesis squared end fraction space equals space fraction numerator straight x minus 2 minus straight x plus 1 over denominator left parenthesis straight x minus 2 right parenthesis squared end fraction space equals space minus fraction numerator 1 over denominator left parenthesis straight x minus 2 right parenthesis squared end fraction
At space straight x space equals space 10 comma space space space dy over dx space equals space minus fraction numerator 1 over denominator left parenthesis 10 minus 2 right parenthesis squared end fraction space equals space minus 1 over 64
which is required slope of tangent to the curve.

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56. For the curve y = 3x2 + 4 x , find the slope of the tangent to the curve at the point whose x-coordrnate is – 2.
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57. Find the slope of the tangent to the curve y = x3 – x + 1 at the point whose x-coordmate is 2.
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58.

Find the slope of the tangent to the curve y = x3 – 3x + 2 at the point whose. x-coordinate is 3. 

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59.

Find the slope of the normal to the curve straight x equals space straight a space cos cubed straight theta comma space space space straight y space equals space straight a space sin cubed straight theta space space space at space straight theta space equals space straight pi over 4.

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60.

Find the slope of the normal to the curve straight x space equals space 1 minus straight a space sin space straight theta comma space space space straight y space equals space space straight b space cos squared straight theta space space at space straight theta space equals space straight pi over 2.

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