Question

For the function $f(x) = 2x^2 −5x$, determine the gradient of the tangent to the curve at the point $x = 6$.

Answer 1

By differentiation, gradient of curve = df/dx = 2(2x) - 5 = 4x - 5

At the point x = 6, gradient of curve = 4x - 5 = 4(6) - 5 = 19

But at a given point on a curve, the gradient of the curve is equal to the gradient of the tangent to the curve.

Therefore the gradient of the tangent to the curve at x = 6 is equal to the gradient of the curve at that point = 19.