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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 \(A\).

80472766e2789434331da8d0e8a59881.png

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 \(g(x)\).

48821463e727f3ec25ffa71821da6a03.png

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 \(x=0\).

\(\text{0}\)