Thread: Find the slope of the tangent to the curve

1. Find the slope of the tangent to the curve

Find the slope of the tangent to the curve

y = 3 + 4x^2 - 2x^3

at the point where x = a.

I have no idea how to answer this question since it doesn't give me any points to work with.

Any help would be greatly appreciated!

2. Differentiate it

$y = 3 + 4x^2 - 2x^3$

$y' = 8x - 6x^2$

y' is also known as the gradient function. so when x = a, the gradient would be equal to? substitute x = a for all x values

$y' = 8(a) - 6(a)^2$

$= 8a - 6a^2$

therefore, the slope of the tangent is equal to $= 8a - 6a^2$