12) 2 1 -3₂ A)x=0, x=3 C) x = 3 x B) Function is differentiable at all points. D) x = 0 13
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- What is the purpose of the Intermediate Value Theorem?How do you find the derivative of f(x) = 5 using the limit definition of derivatives? I know it is 0, but how do I show the work?find the derivative of the function f(x)=x^2 -2x using the definition of the derivative (a process that requires a limit)
- Using the limit definitoin of the derivative, comput the derivative of the function. x^3+3x^2+x+3 b) Which positions x does the graph of y=x^3+3x^2+x+3 have a horizontal tangent line?FIND THE DERIVATIVE OF THE FUNCTION BY THE LIMIT PROCESS. SHOW YOUR STEP BY STEP SOLUTIONS. 3. f(x)= √x+2 4. f(x)= √3x²Find the derivative of the function by the limit process. f(x) = 6/x^2
- Find the derivative of f(x) = 1/√(x + 1) at x = 0 using the definition of the derivative as a limit. Be sure to justify your computations. Specifically, if at any point you evaluate a limit by inserting a value, explain WHY it is possible to do that.1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation of the line tangent to the graph of f (x) at x = 3.use the definition of the derivative to compute the derivative of the function f(x)=1−2x2 at an arbitrary point x. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). f′(x)=limh→0(f(x+h)−f(x)h)=limh→0( )= .