How do you find the slope of the tangent to the curve $y = 3 + 4 x^{2} - 2 x^{3}$ $y = 3 + 4x^2 - 2x^3$ where x = a?

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Answer 1 · 2015-04-07T01:15:17

The derivative of a function is the slope of the tangent to that function.

Given
$y = 3 + 4 x^{2} - 2 x^{3}$ $y=3+4x^2−2x^3$

$\frac{d y}{d x} = 8 x - 6 x^{2}$ $(dy)/(dx) = 8x -6x^2$

So the slope of the tangent to the curve at $x = a$ $x=a$ is
$8 a - 6 a^{2}$ $8a -6a^2$

How do you find the slope of the tangent to the curve y=3+4x2−2x3y = 3 + 4x^2 - 2x^3 where x = a?