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.


(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