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Exercises

Exercise 5.8

Determine the average gradient of the curve $$f(x)=x\left(x+3\right)$$ between $$x=5$$ and $$x=3$$.

$$\text{11}$$

Hence, state what you can deduce about the function $$f$$ between $$x=5$$ and $$x=3$$.

Solution not available at present

$$A\left(1;3\right)$$ is a point on $$f(x)=3{x}^{2}$$.

Draw a sketch of $$f(x)$$ and label point $$A$$.

Determine the gradient of the curve at point $$A$$.

$$\text{6}$$

Determine the equation of the tangent line at $$A$$.

$$y = 6x - 3$$

Given: $$g(x) = -x^2 + 1$$.

Draw a sketch of $$g(x)$$.

Determine the average gradient of the curve between $$x=-2$$ and $$x=1$$.

$$\text{1}$$

Determine the gradient of $$g$$ at $$x=2$$.

$$\text{4}$$

Determine the gradient of $$g$$ at $$x=0$$.

$$\text{0}$$