Finding an Equation of a Tangent Line In Exercises 67-74, (a) find in equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. f ( x ) = 1 2 x ln x 2 , ( − 1 , 0 )
Finding an Equation of a Tangent Line In Exercises 67-74, (a) find in equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results. f ( x ) = 1 2 x ln x 2 , ( − 1 , 0 )
Finding an Equation of a Tangent Line In Exercises 67-74, (a) find in equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results.
Finding a Derivative In Exercises 17–42, findthe derivative of the function.
\text { 17. } f(x)=\arcsin (x-1)
Relativity According to the Theory of Relativity, the length
L of an object is a function of its velocity v with respect to an
observer. For an object whose length at rest is 10 m, the func-
tion is given by
L(v) = 10,/1-
where c is the speed of light (300,000 km/s).
(a) Find L(0.5c), L(0.75c), and L(0.9c).
(b) How does the length of an object change as its velocity
increases?
Equation of a tangent line Let f(x) = -16x 2 + 96x (the position function examined in Section 2.1) and consider the point P(1, 80) on the curve.
a. Find the slope of the line tangent to the graph of f at P.
b. Find an equation of the tangent line in part (a).
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.