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The function h is defined by
Find h′(x).
Determine the gradient of the curve y=h(x) at x=2.
Determine the equation of the tangent to y=h(x) at x=2 in the form ax+by+d=0, where a,b,d∈Z.
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Consider the function
which has a local maximum at x=1.
Show that k=9.
Find the coordinates of the local minimum.
State the interval on which the gradient of the curve is negative.
Determine the equation of the normal to the curve at x=2, in the form y=mx+c.
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Consider the function
and the following tables of values as x approaches 3 from below.
State x→3limf(x).
Explain why f(3) is undefined.
Determine the value of k.
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