Question

if f(x)=3x+2find f'(-2) from find first principle

Answer 1

check the attachment

Answer 2

The value is  f'(-2)= 3.

Step-by-step explanation:

Given : If f(x)=3x+2

To find : f'(-2) from first principle ?

Solution :

f(x)=3x+2

According to first principle,

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

Applying on given function,

$f'(x)= \lim_{h \to 0} {\frac{3(x+h)+2-(3x+2)}{h}}$

$f'(x)= \lim_{h \to 0} {\frac{3x+3h+2-3x-2}{h}}$

$f'(x)= \lim_{h \to 0} {\frac{3h}{h}}$

$f'(x)= \lim_{h \to 0} {3}$

$f'(x)= 3$

Therefore, f'(x)= 3

⇒ f'(-2)= 3

Hence, the value is  f'(-2)= 3.

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