###### Software-Engineering

October 14, 2023###### GATE 2017 [Set-1]

October 14, 2023# GATE 2007

Question 1 |

Consider the following two statements about the function f(x)=|x|

P. f(x) is continuous for all real values of x Q. f(x) is differentiable for all real values of x

Which of the following is TRUE?

P is true and Q is false. | |

P is false and Q is true. | |

Both P and Q are true. | |

Both P and Q are false. |

Question 1 Explanation:

f(x) = |x|

→ f(x) is continuous for all real values of x

For every value of x, there is corresponding value of f(x).

For x is positive, f(x) is also positive

x is negative, f(x) is positive.

So, f(x) is continuous for all real values of x.

→ f(x) is not differentiable for all real values of x.

For x<0, derivative is negative

x>0, derivative is positive.

Here, left derivative and right derivatives are not equal.

→ f(x) is continuous for all real values of x

For every value of x, there is corresponding value of f(x).

For x is positive, f(x) is also positive

x is negative, f(x) is positive.

So, f(x) is continuous for all real values of x.

→ f(x) is not differentiable for all real values of x.

For x<0, derivative is negative

x>0, derivative is positive.

Here, left derivative and right derivatives are not equal.

Correct Answer: A

Question 1 Explanation:

f(x) = |x|

→ f(x) is continuous for all real values of x

For every value of x, there is corresponding value of f(x).

For x is positive, f(x) is also positive

x is negative, f(x) is positive.

So, f(x) is continuous for all real values of x.

→ f(x) is not differentiable for all real values of x.

For x<0, derivative is negative

x>0, derivative is positive.

Here, left derivative and right derivatives are not equal.

→ f(x) is continuous for all real values of x

For every value of x, there is corresponding value of f(x).

For x is positive, f(x) is also positive

x is negative, f(x) is positive.

So, f(x) is continuous for all real values of x.

→ f(x) is not differentiable for all real values of x.

For x<0, derivative is negative

x>0, derivative is positive.

Here, left derivative and right derivatives are not equal.

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