For the equation y = 1/2x^4 + x; a = 2: a) Find an equation of the tangent line at x = a. b) Use a graphing utility to graph the curve and the tangent line on the same set of axes

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

A:

Q: compare a secant and a tangent by defining each.

A: To compare a secant and a tangent

Q: 4) Determine an equation for the tangent to the graph of the curve y = (6x - 3)(-x? + 2) when x = 1.…

A: Note: To draw the tangent of a curve at a given point, first we have to find out the slope of the…

Q: Illustrate the tangent line of the curve.

A: Given,

Q: (c) Find the slope of the curve x?y + xy? = 6 at the point (2, 1).

A: Slope of a curve is given as dy/dx. Pount given is (2,1)

Q: Find the points on the curve y = 2r3 – 3x2 – 12x + 20 - where the tangent is parallel to the x-axis.

A: A straight line parallel to x-axis have slope 0.

Q: Find the equation of the tangent line to the curve y = 4x-8 at the point (3.-2).

A:

Q: Each of two tangents to the circle x² + y² = 25 has a slope 2. Find the points of contact.

A:

Q: Construct your own curve (function) with its tangent line. Graph your function and its tangent line…

A: Here we have to construct the curve (function) with its tangent line. and Graph the function and its…

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A:

Q: (1- x) (1+x) Find an equation of the tangent line to the curve y = at (-2, -3).

A:

Q: Write the equation of a circle osculating with the curve f(x)=arctanx at the point x0=1.

A: The curve fx=arctanx. We have to find the equation of an osculating circle at the point x0=1.