Write the equation of the tangent line to the curve at the indicated point. As a check, graph both the function and the tangent line. (Use exact numerical values. Do not round.)
$$ f(x)=\frac{x^{7}}{7}-\frac{7}{x^{7}} \text { at } x=-1 $$
Write the equation of the tangent line to the curve at the indicated point.
Find an equation for the line tangent to the curve at the point defined by the given value oft. Also, find the value of dy at this point x=++ cost, y = 1 + 2 sin tt-7 Write the equation of the tangent line. y=-x+ (Type exact ahswers, using as needed)
11.2.11 Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point. x=t-sin ty=1 - 3 cos tt Write the equation of the tangent line. y= x+ (Type exact answers, using a as needed.)
Solve the problem. 1) Write an equation for the tangent line to the curve x2 - 5xy + y2 = 7 at the point (-1, 1). Compute the gradient of the function at the given point. 2) f(x, y, z) = -5x - 9y + 10%, (3, 4,-2)
For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of x. Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct. [T] f (x) = 5 cot x, x = T 4.
Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point x=16 cost, y = 4 sint,t= The equation represents the line tangent to the curve at t= (Type an exact answer, using radicals as needed.) d²y The value of dx2 (Type an exact answer, using radicals as needed.) att =
d²y Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point dx x= 16 cost. y = 4 sint, t = 7 л 2 The equation represents the line tangent to the curve att (Type an exact answer, using radicals as needed.) dy The value of att is dx? (Type an exact answer, using radicals as needed.) 70 4
(1 point) Find the equation of the line tangent to the graph off at the indicated x value. y = 10 sin-1 3x, x = 0 Tangent line: y =
Find an equation of the line tangent to the curve at the point corresponding to the given value of t. 71 x= cost+t sint, y=sint-tcost;t=4 (Type an equation. Simplify your answer. Type your answer in slope-intercept form. Type an exact answer. Use integers or fractions for any numbers in the equation.)
13) Find an equation of the tangent line to the curve y=sin(5x)+cos(8x) at the point (π/6,y(π/6)). what is the tangent line: 14) f(x)=4x^2cos(4x) what is the first and second derivatives and solve both for F(5) NOTE There should be four answers! 16) Suppose that f(x)=3x/(4−5x^)3 find an equation for the tangent line to the graph of f at x=2. the tangent line: y=
(1 point) Use implicit differentiation to find an equation of the tangent line to the curve 2xy3+xy=302xy3+xy=30 at the point (10,1)(10,1). (1 point) Use implicit differentiation to find an equation of the tangent line to the curve 2xy3 + xy = 30 at the point (10, 1). The equation -3/70 defines the tangent line to the curve at the point (10, 1).