5. a Find the derivativefx)-2x+7x of using the definition of the derivative. (Yo

Question

5. a Find the derivativefx)-2x+7x of using the definition of the derivative. (You can check your answer using rules but not use rules to find the derivative). (10 points) b. Find the derivative when x=1, x-2.using the derivative function from part (a). cWrite the equation of the tangent to the function at x-1 d. Write the equation of the normal to the function at x=-2 6. Match the graphs of the functions A, B, C and D with the graphs of the derivatives from the second row I, II, III and IV. Give reasons for your choice (8 points)

Explanation / Answer

5.a) f(x) =2x^2 +7x

f'(x) =4x +7

b) at x =1

f'(1) =4 +7 =11

at x =-2

f'(-2) =-8 +7 =-1

c) at x =1 f(x) =9

f'(1) =11

y =11x +c

putting x =1 ,y =9

9 =11 +c

c =-2

y =11x -2

d)at x =-2 f'(-2) =-1

f(-2) =-6

y =-x +c

-6 =2 +c

c =-8

y =-x -8

6. A-II

B-III

C-IV

D-I

Thank you

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