Find the slope of the tangent to the curve f(x) = 2x6 + x4 – 1 at x = 1.
Given,
y = 2x6 + x4 – 1
We need to find slope of tangent of f(x) at x = 1.
Slope of the tangent is given by value of derivative at that point. So we need to find dy/dx first.
As, y = 2x6 + x4 – 1
Now, differentiating both sides w.r.t x –
∴ )
Using algebra of derivatives –
⇒
Use:
∴
⇒
As, slope of tangent at x = 1 will be given by the value of dy/dx at x = 1
∴