A population of dolphins is living in an environment with limited resources in such a way that the population (measured in thousands of dolphins) at time t (measured in years after 2013) is given by P(t). a) explain the physical interpretation of P′(1). b) Use the graph provided to make a rough sketch of the graph of P′(t). c)Based on your graph, at (approximately) what time will the population be growing the fastest?

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -5 and g'(3) = 2.…

A: Here, y = g(x)  and g(3) = -5 i.e. when x1 = 3, then  y1 = -5 and g(3)=2 i.e. At x =3, the slope, m…

Q: Two stationary patrol cars equipped with radar are 5 miles apart on a highway, as shown. As a truck…

A: Given: Distance between the two stationary patrol cars is 5 miles Time taken by a truck to cover the…

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from reflecting about…

A: If a function is reflected over the y=x line then (x,y) → (y,x) This means y=ln(x) will become…

Q: If a is a positive integer, then the slope of the tangent to the graph of y = + a ln(ax) at x = 1 is…

A:

Q: Find the x-coordinate(s) of the point(s) at which the graph of g(x)=(2x-1)(x^2 +3) has a tangent…

A: Solution:- Step-by-step solution of the above question is given below. The given graph is…

Q: Let g(x) = x 3. Calculate g'(a), and explain why g' does not exist when a = = 0. Sketch a graph of y…

A: Consider the function: gx=x23g'x=ddxx23Apply the Power Rule:   ddxxa=a⋅xa−1…

Q: The velocity of a skydiver 1in m>s2 t seconds after jumping from a plane is v1t2 = 60011 -…

A: Limits are used where the exact value of the function cannot be determined, hence the approaching…

Q: Let P(t) be the population of a bacteria culture after t days and suppose that P(t) has the line y =…

A:

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -6 and g'(2) = 4.…

A:

Q: 1. Where does the graph of s= t² - 3t+2 have horizontal tangent? Write an equation for the tangent…

A: Topic = Derivative As per guidelines , At a time only one question can be answered out of different…

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -2 and g'(3) = 6.…

A: we are given y=g(x),g(3)=-2,g'(3)=6

Q: Suppose you are studying the graph of a population of a particular species and you determine that…

A:

Q: Given the graph of r sin 2y = y cos 2x pictured at right, what is the point-slope equation for the…

A: The derivative of the function y'=dydx is the measure of how fast the function is changing with…

Q: 50 Find the length of the curve whose equation is given by r = e on 0 < 0 < 2T.

A:

Q: it is known from experiments that the height (in meter) of a certain plant after t months is given…

A: Given: ht=t-t; 0≤t≤1 for finding given values, first we draw graph of given function on given…

Q: 25. The accompanying graph shows the total distance s traveled by a bicyclist after t hours. 40 30…

A:

Q: Question 7 of 18 Find the point (xo, yo) on the graph of y x39x2 3x - 5, at which the slope of the…

A: Given:

Q: 1 Find an equation for the line tangent to the graph of y=2 tan at the point (3,1/8).

A:

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -2 and g'(4) = 3.…

A:

Q: – 80 Find the length of the curve whose equation is given by r = e" on 0 < 0 < 27.

A: We have to find the length of the curve

Q: The tangent line to the graph of y = g(x) at the point (4, 2) passes through the point (1, 8). Find…

A: topic - slope of a tangent line

Q: A ball is dropped from a 200 foot cliff. If gravity is 32 ft/sec2, find the position function of the…

A: Given :- Initial height of ball (S0)= 200 feet Accelaration due to gravity(g) = 32 feet/sec2…

Q: 4) Find a formula for the line tangent to the curve at the point (4,4).

A:

Q: 2r+19 Find all values of x at which the tangent line to the curve y = x+9 has the y-intercept 2.…

A:

Q: A ping-pong ball is caught in a vertical plexigiass column in which the air flow alternates…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -4 and g'(2) = 5.…

A: Given function is                                              y=g(x), at x=2g(2)=-4 and g'(2)=5 we…

Q: 41. Aroller coaster has the shape of the graph in Figure 19. Show that when the roller coaster…

A:

Q: At a certain ocean bay, the maximum height of the water is 4 m above mean sea level at 8:00 a.m. The…

A:

Q: 21 Find the equation of the tangent i ne OF the graph of yEra y= xe at the point ( ). y=? -2X

A: The objective is to find the equation of the tangent line.

Q: Two ships are sailing in the fog and being tracked on a small screen. At some point in time, t=0,…

A: Hi, thank you for the question. Since you have posted a question with multiple sub parts, as per the…

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from reflecting about…

A: Given: y=lnx equation of the graph that reflecting about y-axis will be y=ln-x

Q: 1. a) Find the equation of the tangent line to the curve given by F(t) = (cos(nt), t, 1 + t2), for t…

A: First we find r(2) and r'(2). Then find equation of tangent line to given curve r(t).

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a? + In(az + 1) at a =…

A: To find the slope of the tangent to the graph of the given equation

Q: ind an equation of the tangent line to the graph of the function at the given poin y = (e - 4)2. (0,…

A:

Q: 69. Find a cubic function y graph has horizontal tangents at the points (-2, 6) and (2, 0). = ax +bx…

A: The form of cubic function is given as follows.

Q: 2. Consider the graph of g(x)-2+3-1 a Lt anyalues at which g)net dafferentiable Setch the tangent…

A: Since you have posted a question with multiple sub parts, we will solve the first three subparts for…

Q: 90. The function C(t) = K(ea – eb), where a, b, and K are positive constants and b> a, is used to…

A:

Q: -9x Find an equation of the tangent line to the graph of y = e at the point (4, e¯3º). y =

A: First of all we will find the slope of the tangent line using the fact that the slope of tangent…

Q: The equation for the tangent to the curve y = t+ at the point (1,3

A:

Q: P(t). 2. The population, of a lakeside town with a large number of seasonal residents can be modeled…

A:

Q: The graph of y = fx) and the tangent to the curve at x = 1 is shown below. ..... 5 3 y - f(x) -1 0.

A: Consider the given figure.

Q: 9) Find the point(s), if any, where the graph has a horizontal tangent for 3x4 %3D = - 3x2 f(x) = 4…

A:

Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

A:

Q: The graph of the acceleration a(t) of a car measured in ft/s is shown. Use the Trapezoidal Rule with…

A:

Q: Sketch the graph of y = -3 sin(x) on the axes below. 4 3 2 -7/2 7/2 37/2 27 -1 -2 -3 -4

A:

Q: Graph the curve over the given interval together with its tangent at the given value of x. Graph the…

A:

Q: Draw a sketch of a position-time graph, corresponding velocity-time graph, and corresponding…

A: we have to use following relation between f , f' and f" * when f'(x) &gt;0 =&gt; function increasing…

Q: The curve with equation y= e* In(x- 1) has a stationary point when x = p. (i) Show that p satisfies…

A: Given- The curve with equation y = e-2x lnx - 1 has a stationary point when x = p. To Show- Show…

Q: 3. Find y' and the equation of the tangent line to the graph of In(ay) = y²-1 at (1,1). 11: 11:

A: We have to find y' and equation of tangent

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -6 and g'(4) = 3.…

A: The tangent line is a Straight line which is a tangent to the curve at the point. The point here…