Evaluate y' when x = 1

Question

Consider the following.

y = x⁴ − 3x² + 8

Evaluate y'' when x = 1

y' (1) = ?

Write the equation of the tangent line to the curve at x = 1.

 ?

Answer 1

If y = x⁴ - 3X² + 8

y'(x) = 4x³ - 6x

Evaluated at 1, y'(1) = 4-6 = -2

Similarly differentiating again:

y''(x) = 12x² - 6 so y''(1) = 6