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Consider the function F(x)=17(x^4)+13(x^3)+12(x^2)+7x+2. A) differentiate F(x) B)What is the gradient at the point (2,440)

A point of notation: '#' is the beginning of a comment, we will use comments to note down thoughts and tricks at each stage of the problem A) let f(x) denote the differential of F(x) F(x)=17(x^4)+13(x^3)+12(...
DW
Answered by Dylan W. • Maths tutor
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Find the stationary points of the equation. f(x)=3x^2+4x.

Stationary points are points on the graph where the gradient is equal to 0.The gradient for any given point can be calculated by differentiating the original equation.f(x)=3x^2+4xDifferentiating gives:=> ...
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Answered by Ethan W. • Maths tutor
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i) differentiate xcos2x with respect to x ii) integrate xcos2x with respect to x

i) For this question we need to use the product rule as there are two functions that are being multiplied together Product Rule: (uv)'=u'v + v'u Apply this formula to the problem: xcos2x => u=x, u'=1 =&gt...
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Answered by Carina P. • Maths tutor
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How do we know the derivative of x^n

What does derivative mean? The derivative of a function the represents the gradient of the function for each value of x. Remark that the gradient of a function at point (x,f(x)) is equal to the gradient of a...
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Answered by Thomas P. • Maths tutor
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If f(x)=7xe^x, find f'(x)

f(x) = 7xe x Using the product rule: [f'(x)=u*(dv/dx)+ v*(du/dx)]Let u=7x and v=e x Therefore, du/dx=7 and dv/dx=e x Hence, f'(x) = 7xe x + 7e x
LM
Answered by Lanya M. • Maths tutor
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