Problem 7d Define f(x) = x3 + 2x + 1 for all x. Find the equation of the tangent
ID: 2983849 • Letter: P
Question
Problem 7d
Define f(x) = x3 + 2x + 1 for all x. Find the equation of the tangent line graph of f:R rightarrow R at the point (2, 13). For m1 and m2 numbers, with m1 m2, define f(x) Prove that the function f:R rightarrow R is continuous but not differentiable at x = 0. Use the definition of derivative to compute the derivative of the following functions at x = 1: f(x)= for all x>0. F(x) = x3 + 2x for all x. f(x) = 1/(1 + x2) for all x. Evaluate the following limit s or determine that they do not exist: x2/x x2-1 x-1 x4-16/x-2 Let I and J be open intervals, and the functions f:I rightarrow R and h:J have the property that h(J) C I, so the composition f 0 h:J rightarrow R is defined. Show that X0 is J, h: J rightarrow R is continuous at X0, h(x) h(x0) if x x0, and f:I rightarrow f is differentiable at h(X0), then f(h(x))-f(h(x0))/h(x) - h(x0) = f'(h(x0)). Use Exercise 6 to show that f: R rightarrow R is differentiable at x0=1, these: f(1 + h)-f(I)/h = f'(1) f( t)-f(I)/ t-1 = f'(1) f(x2)-f(1)/ x2-1=f'(1) f(x2)-f(I)/x-1 = 2f'(1) f(x3)-f(I)/x-1 = 3f'(1). (Hint: For the last two limits, first make use of the difference of powers formula) For a natural number n 2,defineExplanation / Answer
Using L Hospital Rule
Lim x--> 1 2xf'(x^2)/1
Lim x--> 1 2xf'(x^2)
putting x=1
we get 2f'(1)