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Find the stationary point of the curve y = -2x^2 + 4x.

Firstly, since we have a negative coefficient of x^2, we know we are looking for a maximum point. It is also always helpful to draw a sketch so you know what's going on. Whiteboard sketch. Now to find the st...
LJ
Answered by Luke J. • Maths tutor
6344 Views

The Curve C has equation y = 3x^4 - 8x^3 - 3. Find dy/dx.

The question is asking us to differentiate the equation y = 3x^4 - 8x^3 - 3. To differentiate this equation, we must differentiate term-by-term. In order to differentiate a term, we must multiply the coeffic...
DC
Answered by Dharmik C. • Maths tutor
6884 Views

Proof by Induction - "What's the point if we already know the answer?"

I'll try to use carefully chosen examples to explain the advantages/disadvantages of induction as a method of proof. My answer will go roughly as follows: Advantages: Sometimes the only obvious method of pro...
RH
Answered by Ruben H. • Maths tutor
4791 Views

Differentiate y = 15x^3 + 24x^2 + 6 with respect to x.

To differentiate y with respect to x, you have to multiply each x term by their respective power and then decrease their power by one. For example, 4x 2 differentiated is 2 x 4x 2-1 = 8x. So, splitting this ...
DM
Answered by Dominic M. • Maths tutor
4220 Views

What the integral of e^2x*x? (limits 0,1)

Whenever you see an integral with a product as the integrand, check if integration by parts works. That is, Int(v(x)*u'(x)) = u(x)v(x)-int(u(x) v'(x)) So you should see that its easier to call v(x)=x and u'(...
OO
Answered by Oliver O. • Maths tutor
4533 Views