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

∴