1.5 Exponentials and logarithms

A curve has the equation $y = e^{2x}$

a.

Find, in terms of $a$ , the equation of the tangent to the curve at the point $a, e^{2a})$

[3]

b.

Find the value of $a\,$ for which this tangent passes through the origin.

[2]

c.

Hence, find the set of values of $m\,$ for which the equation $e^{2x} = mx$ has no real solutions.

[3]

A curve has the equation $y = e^{2x}$

a.

Find, in terms of $a$ , the equation of the tangent to the curve at the point $a, e^{2a})$

[3]

b.

Find the value of $a\,$ for which this tangent passes through the origin.

[2]

c.

Hence, find the set of values of $m\,$ for which the equation $e^{2x} = mx$ has no real solutions.

[3]

1.5 Exponentials and logarithms Questions