1. Find the derivative of the function using the definition of derivative.
(a) \(f(x)=\sqrt{7-3x}\)
Solution
(b) \(f(x)=3+2x-x^2\)
Solution
(c) \(\displaystyle f(x)= \frac{1}{1+2x}\)
Solution
2. The graph of f is given below. State, with reasons, the numbers at which f is not differentiable.
Solution
3. The graph of f is given below. Evaluate the following, if they exist. Otherwise, state so.
![y=f(x) y=f(x)](graph5.png)
(a) \(f^{\prime}(-4) =\)
(b) \(f^{\prime}(-3) = \)
(c) \( f^{\prime}(-2) =\)
(d) \( f^{\prime}(-1.5) =\)
(e) \( f^{\prime}(-1) =\)
(f) \( f^{\prime}(0) =\)
(g) \( f^{\prime}(1) =\)
(h) \( f^{\prime}(2) =\)
(i) \( f^{\prime}(3) =\)
(j) \( f^{\prime}(4) =\)
Solution