How do you find f'(x) using the definition of a derivative for f(x)=−7x2+4x?

It isf′(x)=limh→0(f(x+h)−f(x)h)⇒f′(x)=limh→0−7⋅(x+h)2+4(x+h)−(−7x2+4x)h⇒f′(x)=limh→0(−h(7h+2⋅(7x−2))h)⇒f′(x)=limh→0(−(7h+2(7x−2)))⇒f′(x)=−14x+4

"How do you find f'(x) using the definition..." was answered by our community

Cazzaoro0w9

2022-04-16

How do you find f'(x) using the definition of a derivative for

f (x) = - 7 x^{2} + 4 x

YAMAGAMA699k

Beginner2022-04-17Added 8 answers

It is

f^{'} (x) = lim_{h \to 0} (\frac{f (x + h) - f (x)}{h}) \Rightarrow f^{'} (x) =

lim_{h \to 0} \frac{- 7 \cdot {(x + h)}^{2} + 4 (x + h) - (- 7 x^{2} + 4 x)}{h} \Rightarrow f^{'} (x) =

lim_{h \to 0} (\frac{- h (7 h + 2 \cdot (7 x - 2))}{h}) \Rightarrow f^{'} (x) = lim_{h \to 0} (- (7 h + 2 (7 x - 2))) \Rightarrow f^{'} (x) = - 14 x + 4

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