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Let f(x) = 2x^3 − kx^2 + 2x − k. For what values of the real number k does the graph y = f(x) have two distinct real stationary points? (MAT 2017 q1.A)

A point a is a stationary point if and only if f'(a) = 0. Let's compute the derivative: f'(x) = (2x^3 − kx^2 + 2x − k)' = 6x^2 - 2kx + 2. (-k is a constant so it cancells out) f'(x) = 0 iff 6x^2 -2kx + 2 = 0...
JG
Answered by Jan G. • MAT tutor
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Expand and simplify 3(x+4) - 2(4x+1)

3(x+4) - 2(4x+1)= 3x + 12 - 8x + 2= 3x - 8x + 12 - 2= -5x + 10
PP
Answered by Pioli P. • Maths tutor
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Craig weighs 74.2 kg, Connie weighs 67.8 kg, and Chloe weighs 69.4 kg. What is the range of their weight?

6.4 kg
PP
Answered by Pioli P. • Maths tutor
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What is the chain rule and how is it used?

The chain rule is used to find the derivative of an expression in the form h(f(x)) where you have a function in terms of a function of x for example: h(f(x)) = 2(3x+1)^3 where f(x) = 3x+1 In order to use the...
JB
Answered by Joseph B. • Maths tutor
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Explore gender in H.G. Well’s Ann Veronica.

Ann Veronica’s gender confines her to the private sphere and limits her opportunities. Her academic performance is better than her brother’s, but her father will not let her continue her studies at Imperial ...
MS
Answered by Marissa S. • English tutor
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