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Find the gradient of the tangent to the curve y=4x^2 - 7x at x = 2

First, we differentiate our equation using the power rule:dy/dx = 8x - 7This is the gradient of our tangent, to the original equation, at any point x. So, to calculate the gradient at x = 2, we substitute th...
LA
Answered by Luke A. • Maths tutor
5487 Views

a typical question would be a setof parametric equations y(t) and x(t), asking you to find dy/dx and then the tangent/normal to the curve at a certain point (ie t = 2)

this question is a great example as we have many different aspects of a level maths workng together into one.initialy you will use use chain rule to find dy/dx = dy/du * du/dx.then you will either keep the v...
TS
Answered by Thomas S. • Maths tutor
3542 Views

The equation f(x) =x^3 + 3x is drawn on a graph between x = 0 and x = 2. The graph is then rotated around the x axis by 2π to form a solid. What is the volume of this solid?

f(x) = x 3 + 3x V = π ∫ (f(x) 2 ) dx V = π ∫ 0 2 (x 3 + 3x)(x 3 + 3x) dx V = π ∫ 0 2 (x 6 + 6x 4 +9x 2 ) dx V = π[x 7 /7 + 6x 5 /5 + 3x 3 ] V = 2824/35
ZC
Answered by Zac C. • Maths tutor
3823 Views

Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.

Differentiate wrt x. This leaves dy/dx = 3x^2 + 6x and equate this to 0 as we are looking for stationary points.So, 3x^2 + 6x = 0. Factorise to get x(3x +6) = 0. So x = 0 and x = -2 are the two solutions.Now...
TD
Answered by Tutor169411 D. • Maths tutor
3499 Views

Solve the simultaneous equations: y-2x-4=0, 4x^2+y^2+20x=0

Re-arrange y-2x-4=0 to y=2x+4Substitute y=2x+4 into 4x^2+y^2+20x=0 to get 4x^2+(2x+4)^2+20x=0Expand the brackets to get 4x^2+(4x^2+16x+16)+20x=0Simplify to get 8x^2+36x+16=0Divide by 4 to get 2x^2+9x+4=0Fact...
AH
Answered by Andrew H. • Maths tutor
8197 Views