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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?Given f(x)= x² and g(x)= 4x+1 if x>2 = x²+5 if x≤2 a)use the limit definition of derivative to show that g(2)=4Consider the function y=g(x)=-x2+3. Use the limit definition of the derivative to compute a formula for y=g′(x).
- Suppose that a function ƒ satisfies the following two conditionsfor all real values of x and y:i) ƒ(x + y) = ƒ(x) . ƒ(y).ii) ƒ(x) = 1 + xg(x), where limx→0 g(x) = 1.Show that the derivative ƒ'(x) exists at every value of x and thatƒ'(x) = ƒ(x).For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x2 − 4x + 7. Find limx→4f(x). ⇒If f(x) is a function which is continuous everywhere, then we must have
- for f(x) = 3-x/2x+3 , find the f'(-1) using the limit definition of derivative. then use it to find an equation of the tangent line to the graph of y=3-x/2x+3 at (-1,4) using f'(a)= lim as h->0 f(a+h)-f(a)/hf(x) = x(3x-(9x2+2)1/2). Compute the limit of f(x) as x tends to positive infinity.Let g(x) be a differentiable function. Using the limit definition of the derivative, differentable f(x)=7g(x)+x2