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Given that the curve y = 3x^2 + 6x^1/3 + (2x^3)/3x^1, find an expression for the gradient of the curve.

To find the gradient of a curve, you simply differentiate the equation of the curve. The first thing I like to do in any differentiation question is to simplify each expression where you can i.e. whenever th...
TS
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Let y(x) be a function with derivative y'(x)=x^2-2 and y(0) =7. What is the value of y at x = 3?

Integrate to get y(x) = (1/3)x^3 -2x+c where c is a constant. Substitute in our data 7 =y(0) = (1/3)(0)^3 -2*(0) +c = c. So y(x) =(1/3)x^3 -2x+7 and therefore y(3) = (1/3)(3)^3 -2*3 +7 = 9-6+7 = 10
DB
Answered by Dawn B. • Maths tutor
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Find the area bounded by the curve x^3-3x^2+2x and the x-axis between x=0 and x=1.

To find the area under a curve that is bounded by the x-axis you simply need to integrate the equation of the curve between the limits, so for this equation we will integrate y=x 3 -3x 2 +2x with 1 as our up...
JT
Answered by Jack T. • Maths tutor
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Differentiate ln(x^3 +2) with respect to x

The differential of ln(x) is x^-1 or 1/x. Because we have x^3 + 2 inside the bracket we have to differentiate this term also and multiply this with the other term. For example, d/dx of x^3 +2 is equal to 3x^...
GL
Answered by George L. • Maths tutor
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A curve is defined by the parametric equations: X = 3 – 4t , y = 1 + (2/t) Find (dy/dx) in terms of t.

When dividing fractions by fractions with a common factor: (a/c) / (b/c) = (a/c) * (c/b) = (ac/bc) we can cancel the common factor to get (a/b). So in this question we can do the same: (dy/dt) / (dx/dt) = (d...
EE
Answered by Eddie E. • Maths tutor
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