4. The picture shows the graph of cer-tain differentiable function f(x).(a) Find an equation for the line pass-ing through the given points.(b) Use a ruler to draw the line tan-gent to the graph of f(x) at (0, 3), thenfind an equation for that line32101968123.34

Answered: Image /qna-images/answer/b4fbf439-2341-4b92-8ae0-8ab446f554ad.jpg

Answered: 4. The picture shows the graph of cer-…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Use implicit differentiation to find the equation of the tangent line to the curve xy³ + xy = 2 at the point (1, 1). The equation of this tangent line can be written in the form y = mx + b where m is where b is Question Help: Message instructor Submit Question Jump to Answer and
2x-1 b) Determine the value(s) of x at which the graph of the function f (x) = has a x2 horizontal tangent line
(ii) Make a contour plot of the function z(x, y) = -xy in the xy-plane, by drawing a collection of curves z(x, y) = c for different (positive and negative) values of the constant c. Try and sketch a graph of the function in the space of xyz coordinates (as a check you may want to compare that sketch with a computer/Python graph).
Find the second derivative in it's simplified form. Please show a detailed solution. Thank you.
2. Consider the function f(x) = 4 – x². (a) Draw a sketch of the graph of the function. (b) Find the slope of the secant line connecting the points P(1, 3) and Q(2,0) on the graph. (c) Find the slope of the secant line connecting the points P(1,3) and Q(x,4 – x²). (d) Use algebra to simplify your formula from part (c) as much as possible, assuming that P and Q are distinct points. (e) What value do you get when you plug x = 1 into the simplified expression you found in part (d)? (f) Assume that your answer in part (e) is the slope of the tangent line to the graph y = 4 – x2 at the point P(1,3). Use that information to write an equation for the tangent line to the graph y = 4 – a² at the point P(1,3).
8 Evaluate | sec3x cosec3x dk
#8.) Determine the slope of the tangent at point (1,4) on the graph of f(x) = (9-x²) ²3/ #10.) a) Determine the values of x where the graph of each function has a horizontal tangent i> y=(x²-435 -ii) y= (x³ -x)² to x + 5y -10 = D. #12.3 A tangent to the parabola y=3x²-7x +5 is perpendicular Determine the equation of the tangent. #13.) The line y = 8x tb tangent to the curve y² 2x². Determine the point of tangency and the value of b #29. Find numbers a, b, and c so that the graph of f(x) = ax² + bx tc has and a tangent with Slope 16 where x = 2 x-intercepts at (0,0) and (8.0)

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4. The picture shows the graph of cer- tain differentiable function f(x). (a) Find an equation for the line pass- ing through the given points. (b) Use a ruler to draw the line tan- gent to the graph of f(x) at (0, 3), then find an equation for that line 3 2 1 0 1 2 3. 4