Question

Find the slope of the line tangent to the graph of (f) at x=2
of f(x)=3x^4−4x^2+7.

Answer 1

Just substitute x=2 to the one you've differentiated

Answer 2

\[f'(x)=12x^3-8x \\ \\ f'(2)=12(2)^3-8(2) = 80\]

Answer 3

That's the slope/gradient,

Answer 4

do you how i can find the second part the tangent line 80 would be my slope but where do i get my y and x

Answer 5

From the point slope formula,
\[y-y_1=m(x-x_1)\]
We need y1, we already known m and x1, m=slope
using the value of "x", we can find "y" from the first equation

let y=f(x)
y=3x^4−4x^2+7
y=39

(2,39) m=80
\[y-y_1=m(x-x_1)\]
\[y-39=80(x-2)\]

Answer 6

oh ok so i just get y by itself thanks

Answer 7

Yes