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

Question

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

anonymous · Answer

attachment

.sam. · Answer

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

.sam. · Answer

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

.sam. · Answer

That's the slope/gradient,

anonymous · Answer

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

.sam. · Answer

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.sam. · Answer

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
$$y-y_1=m(x-x_1)$$
$$y-39=80(x-2)$$

anonymous · Answer

oh ok so i just get y by itself thanks

.sam. · Answer

Yes