If the tangent line to y = f(x) at (7, 4) passes through the point (0, 3), find f(7) and f '(7).

1 answer:

4 0

Hello :
f'(7) = the slope of the tangent line : let A(7,4) B(0,3)
the slope is : (YB - YA)/(XB -XA)= (3-4)/(0-7) = -1/-7 = 1/7=f'(7)
the equation of the tangent line is :
y-3 = 1/7 (x-0)
y = (1/7)x+3
the line tangent and the graph of : f passes through the point A(7, 4)
x= 7 y=4 so : f(7) =4

You might be interested in

I am an odd 4-digit number between 5,000 and 5,999. The digit in the thousands place is half

Shkiper50 [21]

You are 5,987. 5 in the thousands place because you are a number in the 5,000s, and also the smallest 2 digit number divided 2 makes 5. 9 in the hundreds place because the biggest 1 digit number is 9. 8 in the tens place because the only single digit number that is a multiple of 4, but not 4, is 8. 7 in the ones place because 9 is the hundreds place, minus 2 is 7.

7 0

3 years ago

Skee ball is a game played by rolling a wooden sphere up a ramp into a series of rings. The wooden ball has a surface area of ab

SVEN [57.7K]

Answer:

Radius of the ball is approximately 6.5 cm to the nearest tenth

Explanation:

The ball has the shape of a sphere

Surface area of a sphere can be calculated using the following rule:

Surface area of sphere = 4πr² square units

In the given problem, we have:

Surface area of the ball = 531 cm²

Substitute with the area in the above equation and solve for the radius as follows:

$531 = 4\pi r^2\\ r^2=\frac{531}{4\pi } = 42.255 \\ \\ r=\sqrt{42.255}=6.5004 cm$ which is approximately 6.5 cm to the nearest tenth

Hope this helps :)

3 0

2 years ago

What is 5 radians converted to degrees? If necessary, round your answer to the nearest degree.

Alinara [238K]

Answer:

286 degrees

Step-by-step explanation:

Your formula would be 5 x 180/π

7 0

3 years ago

Could i please get some help?

stepladder [879]

1: slope = 2/1 or 2
2: slope = 5/-5
3: slope = 3/2
4: slope = 7/-4
5: slope = 3/5
6: slope = 2/-8
7: slope = 6/2 or 3
8: slope = 2/-4
9: slope = 1/6

7 0

2 years ago

Which of the following systems of linear inequalities is represented by the solution graphed below?

sattari [20]

Answer is A, y us smaller/equal to 2 and y is smaller/equal to X

5 0

2 years ago