Question

find ( f(x) ) and ( f(c) ).
function: ( f(x) = (3x^2 - 4x)(8x + 7) )
value of ( c ): ( c = -1 )
( f(x) = \boxed{(6x - 4)(8x + 7) + (8)(3x^2 - 4x)} )
( f(c) = \boxed{2} ) (marked with x)
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Explanation:

Step1: Substitute $c=-1$ into $f'(x)$

Substitute $x=-1$ into $f'(x)=(6x-4)(8x+7)+8(3x^2-4x)$

Step2: Calculate first product term

First compute $(6(-1)-4)(8(-1)+7)$:
$6(-1)-4=-6-4=-10$
$8(-1)+7=-8+7=-1$
Product: $(-10)(-1)=10$

Step3: Calculate second term

Compute $8(3(-1)^2-4(-1))$:
$3(-1)^2-4(-1)=3(1)+4=3+4=7$
$8\times7=56$

Step4: Sum the two results

Add the results from Step2 and Step3: $10+56=66$

Answer:

66