1.

If f'(x) = 12x – 6 and f(1) = 30, f'(1) = 5 find f(x)

Answer»

f'(x) = – 6x + c 

f'(x) = 6x2 – 6x + c 

But f'(1) = 5 

6(1)2 – 6(1) + c = 5 

c = 5 

f” (x) = 6x2 – 6x + 5

∫f” (x) dx = ∫(6x2 - 6x + 5) dx 

f(x) = 6x3/3 - 6x2/2 + 5x + c 

f(x) = 2x3 – 3x2 + 5x + c 

But f(1) = 30 

2(1)3 – 3(1)2 + 5(1) + c = 30 

2 – 3 + 5 + c = 30

c = 26 

f(x) = 2x3 – 3x2 + 5x + 26


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