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Differentiate f(x) with respect to x. Find the stationary value and state if it is a maxima, minima or point of inflection f(x) = 6x^3 + 2x^2 + 1

differentiate 6x^3 + 2x^2 + 1 = 18x^2 + 4x To determine stationary point set second derivative to zero 2nd derivative =36x + 4 36x + 4 = 0 therefore x = -4/36 = -1/9 x is -ve therefore point x = -1/9 is a ma...
HH
Answered by Harry H. • Maths tutor
4161 Views

How do you integrate tan^2(x)?

This is a question which tests your knowledge of how to use trigonometric identities as well as integration. As there is no way to immediately integrate tan^2(x) using well known trigonometric integrals and ...
WL
Answered by Warren L. • Maths tutor
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Why is the derivative of x^2 equal to 2x?

Differentiation is finding the slope of a graph; how steep it is at some point. In this case, we want to find out how steep the graph of x^2 is. To do this, we could look at the slope between two points on t...
LH
Answered by Lawrence H. • Maths tutor
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How would I find the approximate area enclosed by the expression e^x*sin(x)*x^3 on an infinite scale?

The area under a curve is analytically calculated using the integral of the function. The integral of the function above could be calculated using integration by parts twice, considering that 3 functions are...
MW
Answered by Matthew W. • Maths tutor
3543 Views

Can you explain where the "Integration by parts" formula comes from?

Sure. If you remember how to calculate d/dx(uv) then you can understand how integration by parts works. d/dx(uv) = u(dv/dx) + v(du/dx). we can re-arrange this: u(dv/dx) = d/dx(uv) - v(du/dx). Now integrating...
CF
Answered by Christian F. • Maths tutor
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