Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Logarithmic functions - Integration - Applications.
Test Yourself 1.


 

The questions on this page focus using integration of a derivative function to find the equation of the function.

 
Find an equation. 1. The gradient function of a curve f(x) is given by .

The line y = 6x - 2 is a tangent to the curve f(x).

Find the equation of the curve f(x).
Answer.f(x) = 2ln(3x - 2) + 4.
  2. The gradient of the tangent at any point on a curve is given by

.

If the curve passes through the point (1, 5), find the equation of the curve and the coordinates of the point on it with the x-value of e.

Answer.y = 3x + 2 lnx - 1
At x = e, y = 3e + 1.
  3. The second derivative of a curve f(x) is given by .

At x = 2, f '(x) = 0.5 and when x = e, y = - ln 2.

Find the equation of the curve f(x).

Answer.y = -lnx + x + 1 - 2e.