What is the gradient of the tangent line to the curve y = 4x^2 - 7x + 2 at the point where… — JAMB UTME

What is the gradient of the tangent line to the curve $y = 4x^2 - 7x + 2$ at the point where $x = 3$ ?

Answer: 17

The gradient of the tangent line to the curve at

x = 3

is 17.

Differentiating

y = 4x^2 - 7x + 2

gives

\frac{dy}{dx} = 8x - 7

. Substituting

x = 3

yields

8(3) - 7 = 17

Find the derivative of the curve's equation

\frac{dy}{dx} = 8x - 7

The gradient of the curve at any point is given by its first derivative with respect to x.

Evaluate the derivative at x = 3

m = 8(3) - 7 = 17

Substituting the given x-coordinate into the derivative gives the specific slope of the tangent line at that point.

The gradient of the tangent to a curve

y = f(x)

x = a

is the value of the first derivative

f'(a)

Question