*thumb_up*100%

The graphs of y=1.1x and y=x have two points of intersection, while the graphs of y=2^x and y=x have no points of intersection. It follows that there is a real number 1 < p<2 for which the graphs of y=p^x and y=x have exactly one point of intersection and y=x is tangent to y=p^x.

Find the value of p

Determine the coordinates of the single point of intersection y=p^x and y=x. Type the values for the x- and y-coordinates or an approximation.

### Want to see the full answer?

Check out a sample Q&A here*arrow_forward*Check out a sample Q&A here

*star_border*

## Related Calculus Q&A

Find answers to questions asked by students like you.

Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

A: Click to see the answer

Q: The slope of tangent lines to a curve y=f(x) is given by f'(x)=1/√√x +4x^3-1. If the point (1,6) is…

A: Equation of curve

Q: f(x)

A: We will find the equation of tangent.

Q: 4. Find the point on the curve y = 2x² – 12x + 5 where the tangent is horizontal.

A: Click to see the answer

Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

Q: What is the value of the slope of the tangent line to the curve *y+y<=5 passing through the point…

A: Click to see the answer

Q: Of the infinitely many lines that are tangent to the curve y= -Sinxand pass through the origin,…

A: Click to see the answer

Q: Find the points on the graph of y = 1– 5x + 3x² where that tangent line is parallel to the line y –…

A: Click to see the answer

Q: Find the points on the curve y = 2x3 + 3x2 12x + 2 where the tangent line is horizontal. (х, у) %3D…

A: Click to see the answer

*question_answer*

Q: Find the points on the curve y 2x3+ 3x2- 12x + 9 where the tangent line is horizontal. (x, y)…

A: The above question is answered below

*question_answer*

Q: If tangent line to y=f(x) at the point (4,3) also passes through the point (0,2), what is the value…

A: Given: If tangent line to y=f(x) at the point (4,3) also passes through the point (0,2) To find: The…

*question_answer*

Q: The equation of the tangent line to the curve x2 + y = 9, at (6,-16) is %3| 16 y = (x + 6) – 16 6 6…

A: Click to see the answer

*question_answer*

Q: x-1 f(x) = x= 1 at (2₁²) x+1

A: The objective of the question is determine the slope of the line tangent.

*question_answer*

Q: Find the equation of the tangent line to the graph of y = f(x) at r = 3. %3D f(x) = In(x – 6|) y =

A: Click to see the answer

*question_answer*

Q: Find the exact length of the curve on the given interval. Show at least 3 steps to justify your…

A: Click to see the answer

*question_answer*

Q: Find an equation of the tangent line to the curve y = x sq root of x that is parallel to the line…

A: Click to see the answer

*question_answer*

Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

*question_answer*

Q: Find the points on the curve y = 2x3 + 3x2 – 12x + 9 where the tangent line is horizontal. (x, y)…

A: According to the given information it is required to calculate the points on the curve where tangent…

*question_answer*

Q: If the normal to the curve y-f(x) at the point(3,4) makes an angle of Pi with the positive x-axis…

A: Click to see the answer

*question_answer*

Q: Find the equation of tangent lineto the cubic x^3-6x^2+10x+8 parallel to the line y=x

A: Click to see the answer

*question_answer*

Q: Find the point on the line y = x closest to the point (1, 0). Hint: It is equivalent and easier to…

A: Distance between two points in xy-plane can be calculated using the distance formula. For two points…

*question_answer*

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2 ; (2,6)

*question_answer*

Q: Find an equation of the tangent line to the curve y = 2x2 +3 that is parallel to the line 82 – y + 3…

A: Click to see the answer

*question_answer*

Q: The slope of the tangent line to a curve at any point is (5x² - y) ex+y If the curve passes thru…

A: Click to see the answer

*question_answer*

Q: At whhat point on the parabola y = x - 3x-5 is the tangent line parallel to 3x-y 2

A: Given y=x2-3x-5 To find the tangent line parallel to 3x-y=2

*question_answer*

Q: What is the slope of the tangents at x=5 of a circle with a center point (x=4, y=0) and a radius…

A: The given circle has center at (x=4,y=0) and radius (r=2).

*question_answer*

Q: Find the slope of the tangent to a parabola y=x^3 at a point on the curve where x=2

A: Consider the following equation:

*question_answer*

Q: The tangent line to the curve y = 1/3x^3−3x^2+9x+12 is parallel to the line 8x−2y=3 at two…

A: given: the tangent line to the curve y=13x3-3x2+9x+12 is parallel to the line 8x-2y=3 at two points…

*question_answer*

Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

*question_answer*

Q: Find the slope of the tangent line to the parabola y= 2 +x−x^2 at the point (0,2).

A: Simply take the derivative of the given equation and substitute the given point.

*question_answer*

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 36x2 +…

A: Click to see the answer

*question_answer*

Q: What are the values of x where tangent line of graph of f(x)=1/x is parallel to the line y=−5x+4.…

A: Follow the procedure given below.

*question_answer*

Q: If the normal to the curve y=f(x) at the point(3,4) makes an angle of ¾Pi with the positive x-axis…

A: Answer of the provided qn in written has been provided below -

*question_answer*

Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

*question_answer*

Q: Find the slope of the function F(x) = √√x+1 at the oint (8,3) And find the equation of the tangent…

A: Click to see the answer

*question_answer*

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – 3x and…

A: Click to see the answer

*question_answer*

Q: Find two integer values of b so that y = -x +b is an equation of a tangent line to the graph of y =…

A: Click to see the answer

*question_answer*

Q: How do I find the shortest distance between the curves y=x^2 and y=ln(x)? Note: I've already asked…

A: Given that, y=x2 and y=ln x

*question_answer*

Q: Find where the tangent line to y= (5x-1)2 (4x+7)3 is horizontel.

A: Click to see the answer

*question_answer*

Q: Find the point in the first quadrant where the line y=2x intersects a circle of radius 3 centered at…

A: Click to see the answer

*question_answer*

Q: The equation of tangent line to y =2rsinx at the point (T) is : Select one: a. y=2x O by=-2x+27 O…

A: Click to see the answer

*question_answer*

Q: The slope of the tangent line to a curve at any point is (5x² - y) ex+y If the curve passes thru…

A: Click to see the answer

*question_answer*

Q: Find the equation tangent line at a=2 for f(x)=2x²-3x+1 O y=15x-7 O None of these O y=5x+7 O y=5x-7

A: Click to see the answer

*question_answer*

Q: Find the equation of the line tangent to the graph of y=4ln(x) at x=3.

A: Equation of tangent line

*question_answer*

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

*question_answer*

Q: Find the point where the tangent line to y = 5x at x = 0.5 crosses the x-axis.

A: Click to see the answer

*question_answer*

Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

A: Click to see the answer

*question_answer*

Q: How many lines are tangent to both of the circles x2 + y2 = 4 and x2 + (y − 3)2 = 1? At what…

A: Given: The equations of circle are given as, Consider the parametric co-ordinates for the Eq. (A)…