# Calculus

posted by .

Find the constants a and b such that the function is continuous on the entire line

f(x){7, x is less than or equal to -3
ax+b, -3 is less than x is greater than 4
-7, x is less than or equal to 4

• Calculus -

you need a smooth transition from (-3,7) to (4,-7)

y-7 = -14/7 (x+3)
or
y = -2x + 1

so, a=-2, b=1

## Similar Questions

1. ### Math/Calculus

Find k so that the following function is continuous on any interval: f(x)= kx 0 (less than or equal to) x (less than) 2 3x^2 2 (less than or equal to x) i know the answer is 12 but i don't know how to arrive at that. could you please …
2. ### stats

Continuous Random Variable, I Let X be a random number between 0 and 1 produced by the idealized uniform random number generator described. Find the following probabilities: a.P(0less than or equal to X less than or equal to 0.4) b.P(0.4 …
3. ### ap stats

Continuous Random Variable, I Let X be a random number between 0 and 1 produced by the idealized uniform random number generator described. Find the following probabilities: a.P(0less than or equal to X less than or equal to 0.4) b.P(0.4 …
4. ### calculus

Find the constants a & b such that the function f(x)={2 if ≤ -1 {ax+b if -1<x<3 {-2 if x ≥3 is continuous on the entire real line
5. ### calculus

Consider the function f(x)=65x−cos(x)+2 on the interval 0 less than or equal to x less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k?
6. ### calculus

find the constants a and b so that the function is continuous on the entire real line. F(x)= 3, x≤-1 ax+b, -1<x<2 -3,x≥2 Help?
7. ### Calculus

In the next questions, a particle is moving along a horizontal line according to the formula: s=2t^4-4t^3+2t^2-1 a) the particle is moving right when A. 0 is less than t is less than 1/2 B. t is greater than 0 C. t is greater than …
8. ### Calculus

A function f(x) is continuous for all x and has a local minimum at (1,8). Which must be true?
9. ### Calculus check

A function f(x) is continuous for all x and has a local minimum at (1,8). Which must be true?
10. ### calculus

Find the constant a such that the function is continuous on the entire real line g(x)=x^2-a^2/x-a if x doesn't equal a 6 if x=a

More Similar Questions