Find the equation of the line tangent to the graph of f(x)=−2cos(x) at x=π4
Give your answer in point-slope form y−y0=m(x−x0). You should leave your answer in terms of exact values, not decimal approximations.
We are given the function,
Firstly, let us find the value of the function at x=π/4
Now, we differentiating the function with respect to x, we get
Then, the value of the derivative at x=π/4 gives us the slope of the tangent at that point. So, we have
Thus, the tangent to the graph f(x) at x=π/4 passes through the
point
and has slope
Thus the equation of the tangent, in point-slope form is
Simplifying we get
which is our required answer.
Find the equation of the line tangent to the graph of f(x)=−2cos(x) at x=π4 Give your...
3. Find the equation of the tangent line to the graph of f(x) = 3x" – 38x that is perpendicular to the line x - 2y = 6. Express slope and coordinates using exact (radical) form or if using decimal fractions round to at least 3 decimal places. You may leave your equation in point-slope form to save time. (4 points)
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Find the equation of the tangent line to the graph of f(x) at the given point f(x) = 1/32x+32 at (1.8) Show all of your work on paper and submit it on canvas. your won't get any credit for the last answer without submission on Canvas The equation of the tangent line to the graph of f(x) at the given point is
The tangent line to the graph of f(x) at x 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line. A y f(x) X -2 2 3 -2 -3 (a) Find the coordinates of the points P and A P(x, y) A(x, y) (b) Use the coordinates of P and A to find the slope of the tangent line (c) Find f'(1) (d) Find the instantaneous rate of change...
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Find an equation of the tangent line to the graph of f(x)= -5-4x at (2, -21). The equation of the tangent line to the graph of f(x)= -5-4x at (2,-21) is y = - 16x + 11
Find an equation of the tangent line to the graph of f(x)= -5-4x at (2, -21). The equation of the tangent line to the graph of f(x)= -5-4x at (2,-21) is y = - 16x + 11