True or False - Use a LEGIBLE capital letter T or F
[6 marks]
You must explain proper logic or find a counter example for full marks. If a
counter example is not practical please correct the error.
5. Function $f(x) = 2\sqrt{x}$ and its derivative, will have the same domain.
6. The best way to differentiate a function which has a rational coefficient is
by using the quotient rule.
7. The following example shows a correct usage of the chain rule
If $j(x) = h(f(g(x)))$, then $j'(x) = h'(f(g(x)))f'(g(x))g'(x)$
8. If $f(a) = b$, and $f$ is continuous at $P(a, b)$, and $f'(a) = 0$ are all true,
then you may safely conclude that $f$ has either a maximum or a
minimum value at $x = a$.
9. The function $f(x) = -2(4 - 5x)^5$ has only one value of $x$ for which its
derivative is not positive.
10. If a function has a horizontal asymptote, then $\lim_{x \to \infty} f(x)$ exists.
