Question

Write the equation of the line that’s tangent to the given function at x=1 f(x)= two x to the third power minus four x

Answer 1

$f(x)=2x^3-4x$

take the derivitive to find the slope

$f'(x)=3*(2x^2)-2*(4x^0)$

$f'(x)=6x^2-4$

so at x=1, the slope is f'(1)=6(1)^2-4=6-4=2

y=mx+b

y=2x+b

find b

at x=1, f(1)=2(1)^3-4(1)=2-4=-2=y

-2=2(1)+b

-2=2+b

-4=b

equation is y=2x-4