### Calculus Problem: Finding Derivatives and Tangent Lines#### Problem Statement:a. Find the derivative function f' for the function f.b. Find an equation of the line tangent to the graph of f at (a, f(a)) for the given value of a.#### Given Function and Value:\[ f(x) = 2x^2 - 9x + 10 \]\[ a = 2 \]#### Solutions:**a. Derivative Function f'**\[ f'(x) = 4x - 9 \]**b. Tangent Line Equation**To find the equation of the tangent line, we substitute \( a = 2 \) into the derivative function to find the slope at that point. Then, we find the y-coordinate by substituting \( x = 2 \) into the original function.The tangent line equation will be in the form:\[ y = mx + c \]Where \( m \) is the slope and \( c \) is the y-intercept.**Steps to Find the Tangent Line:**1. **Slope of the Tangent Line:** Substitute \( a = 2 \) into the derivative function to get the slope \( m \): \[ f'(2) = 4(2) - 9 = 8 - 9 = -1 \]2. **Point on the Graph:** Substitute \( x = 2 \) into the original function to get the y-coordinate \( f(2) \): \[ f(2) = 2(2)^2 - 9(2) + 10 = 2(4) - 18 + 10 = 8 - 18 + 10 = 0 \]3. **Equation of the Tangent Line:** Using the slope \( m \) and the point (2, 0): \[ y = -1(x - 2) + 0 \] Which simplifies to: \[ y = -x + 2 \]Thus, the equation of the tangent line is:\[ y = -x + 2 \]

Name: ### Calculus Problem: Finding Derivatives and Tangent Lines#### Probl
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: ### Calculus Problem: Finding Derivatives and Tangent Lines#### Problem Statement:a. Find the derivative function f' for the function f.b. Find an equation of the line tangent to the graph of f at (a, f(a)) for the given value of a.#### Given Functi

Answered: Image /qna-images/answer/eafe50a4-0f8d-4aef-81a5-ef73dcfcd40f.jpg

Math

Calculus

a. Find the derivative function f for the function f. b. Find an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. f(x) = 2x - 9x + 10, a = 2 a. f'(x) = |4x- 9 b. y =D

a. Find the derivative function f for the function f. b. Find an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. f(x) = 2x - 9x + 10, a = 2 a. f'(x) = |4x- 9 b. y =D

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 1E

See similar textbooks

Similar questions

Differentiate the function. Then find an equation of the tangent line at the indicated point on the graph of the function. y = f(x)=3+√√1-x, (x,y)= (-3,5) The derivative of the function y = f(x) = 3+√√1-x is What is the equation of the tangent line at (-3,5)? O A. 1 y-5= (x+3) O C. y-5-4(x + 3) B. y-5= 4(x + 3) D. 1 y-5=(x+3)
Which of the following statements is correct? (A) The derivative of a function is not related to the slope of the function in any way. B The derivative of a function at a point is equal to the slope of the function's tangent line at that point. The derivative of a function is always zero. D The derivative of a function at a point is equal to the distance between that point and (0, 0). x3 x2 Consider the function y = + 2x. 3 Find all the intervals for which y is increasing. (A) x > -2 (B) X 1 -2 < x < 1
Implicit Differentiation The equation for the curve graphed to the left is x3 - y3 – 6xy = 0. Keep in mind that y is a function of x. When we take the derivative of y we need to use the chain rule because y depends on x: it may help to write it as Use implicit differentiation to find in terms of the -4 -2 variables x and y.
How to find derivative of tangent line of two equations see image below
Consider the following function and point. (3,5) = (a) Find an equation of the tangent line to the graph of f at the given point. y = (b) Use a graphing utility to graph the function and its tangent line at the point. Use the tangent feature of the graphing utility to confirm your results. (Select the correct graph.) y y 5 10 + 10 -15 -5 15 10 5 10 -10 -5 y 10 -15 DO
Look for three (3) mathematical formulas related to your chosen field like engineering, health science, or technology. Write a brief description or explanation about the use of this formula in that field. Find the derivative of this function (formula) with respect to a specific variable. See the example below. Example: Field: MEDICINE Name of Formula: Young's Rule Age of Child in Years Child's dose = x Adult dose Age of Child in Years + 12 Description: This formula is used to determine the amount of drug dosage for children over 1 year of age up to 12 years. Presentation of the Formula using Variables: [Note: If the formula is already stated in variable form, no need to do this part.] ас y = а or y %3 c + 12 c + 12 where: y = child's dose c = age of child in years a = adult dose Computation of the derivative of y with respect to c This means that a will be considered as constant. For a formula with more than 2 variables, you are free to choose which among the variable or variables will…
Direction: Find the derivatives of the following functions: 4. f(x) = v2x* +3 5. f(x) = (2 x? + 5)-4 (4 x5 + 1)
Please provide me with the solution and work to the question. Please try to dumb it down so I can understand it.
I need a new version with an clear writing not be messy Consider the following (a) Find an equation of the tangent line to the graph of the function at the indicated point. (Use x for the independent variable and y for the dependent variable.) (b) Use a graphing utility to graph the function and its tangent line at the point. Must solve this part as well (c) Use the derivative feature of a graphing utility to confirm your results.
please explain step by step to help me understand