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For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1
For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1 continuous at x = 1?
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Q1
For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1 continuous at x = 1?
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Setting 3(1) + c = 2(1)^2 gives c = -1 for continuity.
Questions & Step-by-step Solutions
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Q
Q: For which value of c is the function f(x) = { 3x + c, x < 1; 2x^2, x >= 1 continuous at x = 1?
Solution:
Setting 3(1) + c = 2(1)^2 gives c = -1 for continuity.
Steps: 8
Show Steps
Step 1: Identify the function f(x) which has two parts: f(x) = 3x + c for x < 1 and f(x) = 2x^2 for x >= 1.
Step 2: To find the value of c that makes the function continuous at x = 1, we need to ensure that the two parts of the function meet at that point.
Step 3: Calculate the value of f(x) when x = 1 using the first part of the function: f(1) = 3(1) + c.
Step 4: Calculate the value of f(x) when x = 1 using the second part of the function: f(1) = 2(1)^2.
Step 5: Set the two results equal to each other: 3(1) + c = 2(1)^2.
Step 6: Simplify the equation: 3 + c = 2.
Step 7: Solve for c by subtracting 3 from both sides: c = 2 - 3.
Step 8: Find the value of c: c = -1.
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