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The derivative of a function describes the gradient, also known as the slope. In the simplest terms, the slope defines the change in y divided by the change in x. So if there is a large increase in y for ...

dy/dx = 2x -2 -12x^(-1/2)

First expand (b-4)(b+5) b²-4b+5b-4*5Simplifyb²+b-20

First multiply the brackets to get: (2x² - 6x + x - 3), Simplify to get: (2x² - 5x - 3), This is then all multiplied by x to get: 2x³- 5x² - 3x.

We first differentiate f(x), and we get f'(x)=2x + 5. We then set this equal to 0 and then solve for x. We get that xmin= -2.5. We check whether this was indeed a minimum, by calculating the second deriva...