Question

Dada a função f, por f(x)=30x³-2/3x²+x-1, calcule: 
a)f'(3) 
b)f'(-6)

Answer 1

$f(x)=30x^3- \frac{2}{3}x^2+x-1 \\ \\ f'(x)=30.3x^{3-1}- \frac{2}{3}.2x^{2-1}+1-0 \\ \\ f'(x)=90x^{2}- \frac{4}{3}x+1 \\ \\ a) f'(3)=90.3^2-\frac{4}{3}3+1 \\ \\ a) f'(3)=90.9-4+1 \\ \\ a) f'(3)=807 \\ \\ b)f'(-6)=90.(-6)^2-\frac{4}{3}(-6)+1 \\ \\ b)f'(-6)=90.36+8+1 \\ \\ b)f'(-6)=3249$