If f' (r) exists, then lim, r f(x) = f(r)

Let f: ℝ → ℝ by f(x) = 1 + x^2 and g: ℝ → ℝ by g(x) = 2^x + 3, calculate the following: (f ○ g)(1)

find derivative using limit definition

Suppose f is a function that satisfies the equation f(x + y) = f(x) + f(y) + x2y + xy2 for all real numbers x and y. Suppose also that. Can you please find f(0) , f'(0) , f'(x)

Suppose f(-2)= 0 g(-2) = 0 f'(-2)=5 g/(-2) = 1 and all functions are continuous. f(x) lim Z-2 g(x)

if f' is continuous, f(3)=0, and f'(3)=7, evaluate lim x to 0  f(3+5x) + f(3+6x)/x

Please explain

If f(x) = 5x² , then f' (x) = lim-0 5(x+h)2 –52? h→0 h True False

Describe the concavity of the graph of f(x) = x2-sin(2x) on the interval [0, π] on(4);concave down on(,) up-G.쁩);concave down onc3) and on(쁩 -) upon (0,음):concave down on (음,-) 12 and on㈩ 11π 12' (쯤T) 7x 11π 12' 12 , π ; concave down on b) concave up on ' 12 7x 11π 12'12 11π 12 ; concave down on [ 0, ' 12 d) concave down on (0, π) e) Oconcave up on (0, -* 12 12

f'(a) = lim h→0 h) - f(a)) ´ f(a+h) − f(a) Be sure you can do that as you will be tested on that skill. If f(x) = 14x + 18, find ƒ'( − 4).