### Shadab test question

# Question

(a) Find the interval where *g**¢ *(*t*) > 0.

(4)

(b) Find the interval where *g**² *(*t*) > 0 and the interval where *g**² *(*t*) < 0.

(5)

(c) Find the value of *t *where the graph of *g *(*t*) has a point of inflexion.

(3)

(d) Let *t** be a value of *t* for which *g**¢ *(*t**) = 0 and *g**² *(*t**) < 0. Find *t**.

(3)

(e) Find the point where the normal to the graph of *g *(*t*) at the point

(*t**, *g *(*t**)) meets the *t*-axis.

# Answer

(a) Find the interval where g (t) > 0. (4) (b) Find the interval where g (t) > 0 and the interval where g (t) < 0. (5) (c) Find the value of t where the graph of g (t) has a point of inflexion. (3) (d) Let t* be a value of t for which g (t*) = 0 and g (t*) < 0. Find t*. (3) (e) Find the point where the normal to the graph of g (t) at the point (t*, g (t*)) meets the t-axis.

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