# Find an example of a point (x,y) on the graph of f(x)=2cos(x) where the tangent line has a slope of exactly 1. Question
Functions Find an example of a point (x,y) on the graph of f(x)=2cos(x) where the tangent line has a slope of exactly 1. 2020-11-07
If u derivate the function f(x) u will have a function [f'(x)] that will give u the slope for any value of x:
so, the derivate of the function $$f(x)=2cos(x) is f'(x) = -2sin(x)$$, now to evalute where the derivate is equal to 1 (the slope that are asking for).
$$1 = -2 \sin(x) -> \sin^{-1} \frac{-1}{2} = \frac{-\pi}{6} = -0.53$$
So the x,y coordinate are (-0.53 , 1.72)

### Relevant Questions Find an example of a point (x,y) on the graph of f(x)=2cos(x) where the tangent line has a slope of exactly 1. Find the function f given that the slope of the tangent line at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. $$f '(x)=5(2x − 1)^{4}, (1, 9)$$ Find the function f given that the slope of the tangent line at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. $$\displaystyle{f} '{\left({x}\right)}={5}{\left({2}{x}−{1}\right)}^{{{4}}},{\left({1},{9}\right)}$$ Show that the inverse of any linear function $$f(x)=mx+b$$, where $$m\neq 0$$, is also a linear function. Give the slope and y-intercept of the graph of f-1 in terms ofm and b. Given that point (x, y) is on the graph of y = 4 - x², express the distance from (3, 4) to (x, y) as a function of x. Which of the following is an equation of the line that has a y-intercept of 2 and an x-intercept of 3?
(a) -2x + 3y = 4
(b) -2x + 3y = 6
(c) 2x + 3y = 4
(d) 2x + 3y = 6
(e) 3x + 2y = 6 What is the slope of a line perpendicular to the line whose equation is x - y = 5. Fully reduce your answer. Find an equation for the line that is tangent to the curve y = x3 - x at the point (-1, 0).
b. Graph the curve and tangent line together. The tangent line intersects the curve at another point. Use Zoom and Trace to estimate the point’s coordinates. Whch of the two functions below has the smallest minimum y-value?
$$f(x)=4(x-6)^4+1, g(x)=2x^3+28$$.
A.There is not enough information to determine.
B. g(x)
C.f(x)
D. The extreme minimum y-value for f(x)and g(x)is - infinity. A line passes through the point (2, 1) and has a slope of $$\frac{-3}{5}$$.
A.$$y-1=\frac{-3}{5}(x-2)$$
B.$$y-1=\frac{-5}{3}(x-2)$$
C.$$y-2=\frac{-3}{5}(x-1)$$
D.$$y-2=\frac{-5}{3}(x-1)$$