3 Part question need help with b and c

Question

A) Graph the function of f(x)=3x^2+6x. (GOT THIS PART COMPLETE)

b.) find f'(x) by determining lim= f(x+h)-f(x)

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h h--> 0

c)find f'(-1) , f'(0) and f'(1)

Answer 1

Step by step explanations for you

Answer 2

f(x) = 3x² + 6x

f(x + h) = 3(x + h)² + 6(x + h) = 3(x² + 2xh + h²) + 6x + 6h = 3x² + 6xh + 3h² + 6x + 6h

f(x) = 3x² + 6x

f(x + h) - f(x) = 3x² + 6xh + 3h² + 6x + 6h - (3x² + 6x) = 3x² + 6xh + 3h² + 6x + 6h - 3x² - 6x = 6xh + 3h² + 6h = h(6x + 3h + 6)

[f(x + h) - f(x)]/h = h(6x + 3h + 6)/h = 6x + 3h + 6

The limit of 6x + 3h + 6 as h approaches zero = 6x + 6

So f '(x) = 6x + 6

To find f '(-1) or any other value of "x" just plug the value into this function.