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Find the gradient of the tangent and the normal to the curve f(x)= 4x^3 - 7x - 10 at the point (2, 8)

y = 4x³ - 7x -10The gradient of the function at any point can be found using its derivative:dy/dx = 12x² - 7The gradient of the function, m₁, at (2,8) is equal to the grad...

Answered by Miss P. • Maths tutor

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What is compound interest?

Interest is the return you get on savings or an investment. Normal interest is when you earn a fixed percentage amount per year on an initial amount. For example an interest rate of 5% on £100 would give ...

Answered by Yasmin A. • Maths tutor

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if f(x) = 4x^2 - 16ln(x-1) - 10, find f'(x) and hence solve the equation f'(x)=0.

f(x) = 4x² - 16ln(x-1) -10, f'(x) = 8x - 16/(x-1), so if f'(x)=0, then 8x - 16/(x -1)=0, 8x(x-1) - 16 = 0, 8x²- 8x - 16 =0, 8(x²- x - 2) = 0, x²- x - 2 = 0, (x...

Answered by Ellie B. • Maths tutor

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You are given a right triangle ABC with angle ABC = 30 degrees and AB equal 7. Then AC and BC are then extended to points D and E so that EDC is a right triangle. Find length DE if BD = 15

First BC needs to be found. That is done by dividing AB by cosin ABC. Then CD is found by subtracting form BD. After that the angle ACB is 90-ABC (because ABC is right triangle). Then because AE and BD in...

Answered by Andrey E. • Maths tutor

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