We will take steps to find the tangent line to the graph of f at the general point (x,f(x)), and use it to find a tangent line with a specific property.

(a) For any point (x,f(x)) on the graph of f, let (x+h,f(x+h)) be another point on the graph of f, where h [cannot]= 0 . The slope of the (secant) line joining the two points (x,f(x)) and (x+h,f(x+h)) can be simplified to the form A/(sqrt(7x+6))+(sqrt(7(x+h)+6)), where A is a constant. Find A.

Answer: A=_____________

b) By considering the slope of the secant line as h approaches 0, find the slope of the tangent line to the graph of f at the point (x,f(x)).

Answer: The slope of the tangent line to the graph of f at the point (x,f(x)) is _____
[answers should be expressed in x]

c) At which point on the graph of f is the tangent line parallel to the line y=7/8x?

Answer: The tangent line to the graph of f at the point (______,________) is parallel to the line y=7/8x.

Solution Summary

This solution thoroughly demonstrates a tangent line at the point.

... 1.5 = 16 the velocity is 16 ft/sec. 4. y=30 + 55x (from question 1) a. y-intercept is 30, slope is 55. b. the slope is larger than 0, so the line slopes upward ...

... b. Sketch the secant line on the above graph to show the average ... Show your tangent line on the graph ... e. Use the derivative to calculate the slope of the tangent ...

... a) Let (x, sin x) be a point on the graph of g near (0,0), and write a formula for the slope of the secant line joining (x, sin x) and (0,0). Evaluate this ...

... Find the slope an y intercept of the line. ... Y= -2/7x -8/5 The slope is_____ The y intercept is 0, ? 1. In 1920 the record for a certain race was 46.8 sec. ...

Existing Slopes and Pairs of Points. ... 2 Find the slope and the y- intercept F(x) = -10x -3 The slope is what? ... c.) Find the year when the record will be 44.18 sec. ...

... b) By considering the slope of the secant line as x approaches 3, find the slope of the tangent line to the graph of f at the point (3,2/-3) The slope of the ...

... 3) Using the formula for the slope of a secant line passing through two points on a curve,. ,. determine this secant line slope formula for the function . ...

... c) Find the year when the record will be 42.5 sec. ... the line is perpendicular to 7x+y=6 so slope of line will be 1/7 (Product of slopes of perpendicular ...

...Slope of the tangent line of f at c is 1 = 2√ 1 = 2√ Since the tangent and secant lines are parallel to each other therefore their slopes are equal. ...