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A curve with equation y=f(x) passes through point P at (4,8). Given that f'(x)=9x^(1/2)/4+5/2x^(1/2)-4 find f(X).

To find f(x) using its derivative, first integrate f'(x) with respect to x using the 'add one to the power and divide by the new power' technique remembering to add the constant c. To make this easier, turn ...
EC
Answered by Em C. • Maths tutor
4299 Views

Integrate the function y = 2x^2 + 3x + 8 with respect to x.

Answer = 2x^3/3 + 3x^2/2 + 8x + CThis is an example of numerical integration from C1. To begin to answer this question, we can integrate each term at a time. To integrate this function, we raise the power of...
MC
Answered by Michael C. • Maths tutor
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How can I find the stationary point of y = e^2x cos x?

At a stationary point of y, dy/dx = 0. Step 1: Let's find dy/dx first by differentiating. To differentiate the product of two functions, we can use the product rule :d(fg)/dx = f * dg/dx + df/dx * g. So dy/d...
MT
Answered by Meg T. • Maths tutor
13495 Views

Find the exact solution to the equation: ln(3x-7) =5

Ln(3x-7)=5 Remove logs from both sides 3x-7=e 5 Rearrange to make x the subject3x=e 5 +7x= e 5 +7 3
LH
Answered by Lily H. • Maths tutor
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Consider the functions f(x) = −x^3 + 2x^2 + 3x and g(x) = −x^3 + 3x^2 − x + 3. (a) Find df/dx (x) and hence show that f(x) has turning points at when x = 2 /3 ± √ 13/ 3 . [5] (b) Find the points where f(x) and g(x) intersect. [4]

a) First differentiate f(x) using standard polynomial derivative rules which gives, df/dx=-3x^2+4x+3. The derivative function gives the gradient of f for any value of x. Turning points occur when the gradien...
GA
7156 Views