Question

Find f '(x) and f '(c)
f(x) = (x3 + 3x)(4x4 + 2x − 3), c = 0

Answer 1

f'(x)=(3x^2+3)(4x^4+2x-3)+(x^3+3x)(16x^3+2)
=12x^6+6x^3-9x^2+12x^4+6x-9+16x^6+48x^4+2x^3+6x
=28x^6+48x^4+8x^3-9x^2+12x-9
f'(0)=0+0+0-0+0-9 = 9