Math Problem Statement
Let π(π₯) = βπ₯. Answer the following questions: a) Use the limit definition of the derivative to find π β²(π₯). b) Find the equation of the tangent line at x = 9
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Calculus
Derivative
Tangent Line
Limits
Formulas
f'(x) = lim(h β 0) [f(x + h) - f(x)] / h
f(x) = βx
f'(x) = 1 / (2βx)
Point-Slope Form: y - y1 = m(x - x1)
Theorems
Limit definition of derivative
Point-slope form of a line
Suitable Grade Level
Grades 11-12
Related Recommendation
Find the Derivative of f(x) = sqrt(x) and Equation of Tangent Line at x = 4
Derivative and Tangent Line of f(x) = βx + 12 at x = 1
Limit of Derivative for Function f(x) = βx at a = 7
Finding Derivative and Tangent Line for f(x) = (5 - x) / (1 - βx) at x = 9
Finding fβ²(7) for f(x) = βx - 6 Using the Definition of a Derivative