Search our library of Maths questions

Top answers

Maths

All levels

Given the function f(x)=λx^3 + 9, for λ other than zero, find the inflection point of the graph in terms of λ. How does the slope of the line tangent to the inflection point changes as λ varies from 0 to 1?

f'(x) = 3λx^2f''(x) = 6λxFor the inflection point (x₀,y₀), it is true that f''(x₀)=0 so 6λx_o=0 => x₀= 0 (since λ cannot be zero)Therefore, the inf...

Answered by Claire D. • Maths tutor

2344 Views

By expressing cos(2x) in terms of cos(x) find the exact value of the integral of cos(2x)/cos^2(x) between the bounds pi/4 and pi/3.

cos(2x)=cos²(x)-sin²(x)=2cos²(x)-1
Therefore:cos(2x)/cos²(x)=(2cos²(x)-1)/cos²(x)=2cos²(x)/cos²(x) - 1/cos

Answered by Hugo F. • Maths tutor

7674 Views

How do I differentiate an expression of the form y = (ax+b)^n?

In order to differentiate this we need to use the chain rule- first let u = ax + b. Then differentiating, du/dx = a. By substituting into the original expression, we can obtain y = u^n. Differentiating th...

Answered by Sam C. • Maths tutor

11310 Views

Find dy/dx if y= sinx/2x+1

The quotient rule will need to be applied here.let u = sinx and let v = 2x+1du/dx = cosx and dv/dx =2thus using the quotient rule: (vdu/dx- udv/dx)/v^2(2xcosx +cosx - 2sinx)/ (2x+1)^2

Answered by Sam T. • Maths tutor

4904 Views

Solve the inequality |4x-3|<|2x+1|.

There are two ways to solve this problem. The easiest way is graphically, but that requires little explanation and I am not sure how to show graphs on here so I will explain it algebraically.Because both ...

Answered by Nathanael H. • Maths tutor

8569 Views