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Find the first derivative of f(x). f(x) = ln(3x^2+2x+1)

The differential of a natural log function gives a fraction where the numerator is the first derivative of what we are taking the natural log of and the denominator is what we are taking the natural log o...

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A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.

(a) i) dy/dx= 2x-2-12x^-1/2ii) d²y/dx²= 2+6x^-3/2(b) Substitute x=4 into dy/dx= 2x-2-12x^-1/2 Show that dy/dx= 0 and state 'hence there is a stationar...

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Work out the cube root of (64x1000).

We are asked to calculate (64x1000)^1/3. We can use the laws of indices to write that expression as 64^1/3x1000^1/3, which is easier to evaluate. To work out 64^1/3...

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f ( x ) = 2 x ^3 − 5 x ^2 + ax + a. Given that (x + 2) is a factor of f ( x ), find the value of the constant a. (3 marker)

If x+2 is definitely a factor, that means when we sub x=-2 in, we should get 0 at the end. So 2(-2)^3 - 5(-2)^2 + a(-2) + a = 0So -16 -20= aso a = -36

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